平衡旋转对称布尔函数的计数

doi:10.3969/j.issn.0255-8297.2012.01.008

Journal of Applied Sciences ›› 2012, Vol. 30 ›› Issue (1): 45-51.doi: 10.3969/j.issn.0255-8297.2012.01.008

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Enumeration of Balanced Rotation-Symmetric Boolean Functions

ZHANG Peng1, FU Shao-jing2, QU Long-jiang1, LI Chao1;2

1. College of Science, National University of Defense Technology, Changsha 410073, China
2. College of Computer, National University of Defense Technology, Changsha 410073, China

Received:2011-02-16 Revised:2011-09-06 Online:2012-02-09 Published:2012-01-30

Abstract

Abstract:

Rotation-symmetric Boolean functions (RSBF) that are invariant under circular translation of
indices have been used as components of different cryptosystems. This paper investigates enumeration of the
balanced RSBFs. Based on some improvements and analysis of the solutions of the correlative equation system,
the lower bound on the number of pr-variable balanced RSBFs is improved, where p is a prime. For a general
odd number n, a lower bound on the number of n-variable balanced RSBFs is provided.

Key words: cryptography, Boolean function, rotation-symmetry, balance, enumeration

CLC Number:

TN918.1

ZHANG Peng1, FU Shao-jing2, QU Long-jiang1, LI Chao1;2. Enumeration of Balanced Rotation-Symmetric Boolean Functions[J]. Journal of Applied Sciences, 2012, 30(1): 45-51.

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Enumeration of Balanced Rotation-Symmetric Boolean Functions

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